Trading cookies with a random walk
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The mathematical problem of determining a gambler’s risk of ruin involves analyzing decisions of only one agent, namely the “gambler”. In this work we consider an extension that introduces two additional players, so called “sellers”. These two new agents can boost the probability of success for the gambler by selling to him (using a jargon borrowed from the theory of excited random walks) a “cookie” which is used to increase the probability of moving forward in the next step. The generalized gambler’s ruin scenario considers an excited random walk on a finite interval of integer line with two “cookie store” locations and unlimited supply of cookies at each. Each time when the buyer (walker) visits a store location, he has an opportunity to decide whether he is willing to consume the cookie or not. We wish to determine the equilibrium prices and cookie store locations in a formal game associated with this generalized gambler’s ruin scenario.